Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2019; 56(3): 585-596

Online first article May 16, 2019      Printed May 31, 2019

https://doi.org/10.4134/BKMS.b180242

Copyright © The Korean Mathematical Society.

Biisometric operators and biorthogonal sequences

Carlos Kubrusly, Nhan Levan

Federal University; University of California

Abstract

It is shown that a pair of Hilbert space operators $V$ and $W$ such that ${V^*W=I}$ (called a biisometric pair) shares some common properties with unilateral shifts when orthonormal bases are replaced with biorthogonal sequences, and it is also shown how such a pair of biisometric operators yields a pair of biorthogonal sequences which are shifted by them. These are applied to a class of Laguerre operators on $L^2[0,\infty)$.

Keywords: biisometric operators, biorthogonal sequences, unilateral shifts, Hilbert spaces

MSC numbers: 42C05, 47B37